I've been through a few tires. Highlights:
Shinko 705 front
Good: Affordably-priced, fine for packed dirt/gravel roads.
Bad: Nothing, really.
Shinko 705 rear
Good: also affordable, also fine for dirt roads lacking deep sand or mud.
Bad: Mediocre durability. 6000 miles at best (I went through 2).
Heidenau K60 Scout front
Good: Great grip, honestly probably overkill for any road I have any business trying on my Vee.
Bad: Expensive, no better durability than the Shinko 705 front (starting to scallop at 11000 miles).
Heidenau K60 Scout rear
Good: Great grip, amazing durability (~12000 miles!) which largely makes up for the higher price.
Bad: Expensive, these are pushing $200 today. Super stiff & kind of a PITA to mount.
Unfortunately, I can't speak to road noise from tires. I just don't hear it, if there is any. I wear dense foam earplugs on nearly all rides, and on the highway I would only hear wind noise anyway.
I also can't speak to use in mud. I was always too afraid of falling over to really find out anything about these tires in deep sand or mud.
Hope this helps.
I'm about to need a new front tire, not sure what I'm going to get. Maybe just another Shinko 705. It's not as exciting as an E-07 or a TKC 80, but I ride so timidly on dirt roads that it probably doesn't make a difference either way. I also can't get a front tire to last longer than ca. 11000 miles, so might as well save a few bucks.
2007 Vee with too many farkles